Geometric object with magnitude (length) and direction.

learn more… | top users | synonyms

1
vote
2answers
265 views

Kinematics Problem

The question asks me to find the angular velocity. Now I do not want you to solve my homework, I want explanation please. It states that the acceleration of point P is $\vec{a}= -3.02 \vec{i} ...
1
vote
2answers
474 views

Potential of surface charge

I have a question about the $ \hat{n} $ in this formula $\sigma = P \dot{}\hat{n}$. Why do sometime in my book they get $\sigma = P \cos{\theta}$ for a sphere. Isn't $\hat{n} = r$ ? And then in ...
0
votes
1answer
845 views

How to find acceleration given position and velocity? [closed]

Sorry for this very simple question but I am still very new to the laws of motion. I am dealing with 2-dimensional vectors in my programming environment and I'm following these slides to learn about ...
2
votes
2answers
78 views

Another question about Shankar's notation

I have another question on the notation in Shankar. I think it's sloppy, but I also may just be misunderstanding it. Again, this is at the very beginning of the math intro. He has: $$a\left| V ...
1
vote
1answer
243 views

Is there a more clever way to apply the cross product of two vectors to magnetism?

I am just beginning to learn magnetism and my book used two ways to define the force caused by the magnetic field, brushing over the latter. The first: $$F = q v B \sin (\theta).$$ And: ...
1
vote
2answers
250 views

Question on notation in Shankar's Quantum Mechanics - math intro on vector spaces

I'm just beginning Shankar's 2nd edition Quantum Mechanics and having some trouble with notation. He defines his vectors as "$\left|V\right>$" . And with a scalar multiplier as "$a\left|V\right>$" . ...
0
votes
2answers
571 views

Question involving Vectors and Forces

This is a question I found in Mechanics for Engineers by Beer & Johnston. A 600-lb crate is supported by the rope and pulley arrangement as shown below. Write a computer program which can be ...
1
vote
1answer
576 views

Bra space and adjoint vectors

If I'm not wrong, a bra, $ \langle \phi_n | $, can be thought as a linear functional that when applied to a ket vector, $| \phi_m \rangle$, returns a complex number; that is, the inner product it's a ...
1
vote
2answers
280 views

Why no basis vector in Newtonian gravitational vector field?

In my textbook, the gravitational field is given by$$\mathbf{g}\left(\mathbf{r}\right)=-G\frac{M}{\left|\mathbf{r}\right|^{2}}e_{r}$$ which is a vector field. On the same page, it is also given as a ...
3
votes
4answers
244 views

How to apply an algebraic operator expression to a ket found in Dirac's QM book?

I've been trying to learn quantum mechanics from a formal point of view, so I picked up Dirac's book. In the fourth edition, 33rd page, starting from this:$$\xi|\xi'\rangle=\xi'|\xi'\rangle$$ (Where ...
5
votes
6answers
2k views

How is gradient the maximum rate of change of a function?

Recently I read a book which described about gradient. It says $${\rm d}T~=~ \nabla T \cdot {\rm d}{\bf r},$$ and suddenly they concluded that $\nabla T$ is the maximum rate of change of $f(T)$ ...
0
votes
1answer
282 views

Finding The Resultant Vector [closed]

A plane is flying southeast at 215 km/h. Suddenly there is a wind from the north at 75 km/h. What is the plane's new velocity with respect to the ground in standard position?
0
votes
2answers
2k views

Find the Unit Vector of a Three Dimensional Vector

How can I find the unit vector of a three dimensional vector? For example, I have a problem that I am working on that tells me that I have a vector $\hat{r}$ that is a unit vector, and I am told to ...
0
votes
2answers
2k views

Vertical component of moving weight at a 45 degree angle

Here's an easier one. I use the leg press machine at the gym so I don't have to worrying about hurting myself while lifting heavier weight. The weight glides on a track that looks to be 45 degrees. ...
2
votes
2answers
3k views

split gravitational force into x, y, and z componenets

I am writing a program for a computer science class in which I am doing an n-body simulation in 3-dimensional space. Currently, I have figured out the gravitational force along the hypotenuse between ...
1
vote
2answers
748 views

What is the physical meaning of a product of vectors?

My teacher told me that Vectors are quantities that behave like Displacements. Seen this way, the triangle law of vector addition simply means that to reach point C from point A, going from A to B ...
2
votes
1answer
16k views

How Does force relate to velocity

I had originally asked this question on math overflow and it was suggested that I ask it here. So I know that a force will change the magnitude of velocity if it is at an angle other that 90 degrees. ...
4
votes
2answers
515 views

Is (0,0,0) an undefined vector?

I'm not sure what to make of the direction of a vector with components (0,0,0). Is it an undefined vector?
2
votes
0answers
97 views

Surface normal on the earth to the sun at a given point in time

How complicated is it to calculate a surface normal on the spherical approximation of the earths surface pointing towards the sun at a given point in time? What I try do is to highlight a small area ...
3
votes
3answers
52k views

Linear acceleration vs angular acceleration equation

I'm learning about angular velocity, momentum, etc. and how all the equations are parallel to linear equations such as velocity or momentum. However, I'm having trouble comparing angular acceleration ...
0
votes
1answer
330 views

Calculating vector of plane resulting from tailwind

In some basic physics homework I have, it asks what the resulting vector would be for a plane traveling at x m/s in y direction that is affected by a tailwind going in z direction at w m/s. How would ...
0
votes
1answer
219 views

What causes a gyroscope to eventually rotate/fall over?

Hey so I've just learned about angular velocity and momentum and how torque changes it. Looking at a wheel spinning around an axis, with one end being held up by a rope, what causes the wheel to ...
1
vote
3answers
13k views

Uses of Vectors In Real Life

I always wonder how vectors are used in real life.Vectors and decomposition of vectors,dot and cross products are taught in the early stage in every undergraduate physics course and in every ...
1
vote
2answers
407 views

Vectors, Component Addition, and Significant Figures

I have two vectors $\vec{A}$ and $\vec{B}$ and I need to find the x- and y-components of $\vec{C} = \vec{A} + \vec{B}$. Here's what I have so far: $$|\vec{A}| = 50.0 \mathrm{m}, \theta = ...
0
votes
2answers
506 views

Acceleration vector - deceleration vs direction

If acceleration of something $= - 10 \text{ m s}^{-2}$ And forwards is define as north. Does that mean the object is getting slower (decelerating) or accelerating in the reverse direction (south) ...
14
votes
5answers
9k views

How can area be a vector?

My professor told me recently that Area is a vector. A Google search gave me the following definition for a vector: Noun: A quantity having direction as well as magnitude, esp. as determining ...
13
votes
6answers
23k views

What is the physical significance of dot & cross product of vectors? Why is division not defined for vectors?

I get the physical significance of vector addition & subtraction. But I don't understand what do dot & cross products mean? More specifically, why is it that dot product of vectors ...
5
votes
1answer
265 views

What does scalar phi represent in spacetime?

Trying to understand one-forms and vectors via Schutz's A First Course In General Relativity. His example uses a spacetime diagram, a scalar field phi, a curve (worldline) parametrized using proper ...
-5
votes
1answer
241 views

What is a simple physics application of the reciprocal of a square root? [closed]

I learned yesterday that the inverse of square roots is used to calculate the vectors of surface normals in 3d graphics. It seems like such a mind-bogglingly simple idea, and it leads me to wonder if ...
2
votes
2answers
564 views

Nature of spacetime 4-vector and tangent space?

An entry level confusion about spacetime. I understand that a 4-vector describes a point or event in spacetime. But I've also read (Bertschinger, 1999) that re spacetime "we are discussing tangent ...
1
vote
2answers
3k views

The resultant of two forces acting at any angle?

I am studying about forces as vectors. And they give me this equation: $c^2 = a^2 + b^2 - 2ab \cos C$ Can anybody explain me the second part of the equation? I perfectly understand $c^2 = a^2 + b^2$ ...
4
votes
1answer
1k views

Uniqueness of Helmholtz decomposition?

Helmholtz theorem states that given a smooth vector field $\pmb{H}$, there are a scalar field $\phi$ and a vector field $\pmb{G}$ such that $$\pmb{H}=\pmb{\nabla} \phi +\pmb{\nabla} \times \pmb{G},$$ ...
0
votes
3answers
1k views

Direction of Magnetic force from a current running through a coil of wire

What is the direction is the magnetic force vectors pointing from a coil of wire that has current running through it? ...
8
votes
6answers
1k views

Quaternions and 4-vectors

I recently realised that quaternions could be used to write intervals or norms of vectors in special relativity: $(t,ix,jy,kz)^2 = t^2 + (ix)^2 + (jy)^2 + (kz)^2 = t^2 - x^2 - y^2 - z^2$ Is it ...
0
votes
2answers
317 views

vector cross products

Lets say you have a free particle in a rotating frame of reference with constant angular velocity $\mathbf{\omega}$. By free, I mean there are no real forces on it. Lets call the moving system ...
0
votes
2answers
604 views

Understanding weight on an inclined plane

I'm trying to solve a problem where I have an object resting on an inclined plane, with the angle of the plan being alpha, and the weight being w. I'm having trouble figuring out how I can calculate ...
-1
votes
3answers
3k views

Vector product in 2 dimensions [closed]

If I have a vector A=4i+3j and B=5i-2j, how can I find the vector product AxB? I know that given the angle, its C=AB sin theta, but how can I solve this without the angle?
7
votes
3answers
3k views

Physics of a skateboard ollie

Does anyone have a good explanation of the physics and vectors of force involved in the skateboarding trick the ollie (where the skater jumps and causes the skateboard to rise off the ground with ...
1
vote
3answers
1k views

Can vectors in physics be represented by complex numbers and can they be divided? [closed]

Below is attached for reference, but the question is simply about whether vectors used in physics in a vector space can be represented by complex numbers and whether they can be divided. In ...
2
votes
3answers
692 views

negative vectors (eg velocity)

If you said someone had a velocity of -12mph and they were traveling north? Wouldn't it mean that they were traveling 12mph south? This is a quote from here: if something [object-x] moving to the ...
8
votes
5answers
2k views

How is it that angular velocities are vectors, while rotations aren't?

Does anyone have an intuitive explanation of why this is the case?